PrepTest 129, Section 4, Question 23

Purpose of ParagraphDifficulty3 of 5
Passage 4Fractal geometry, self-similarity, and the debate over mathematical rigor
The questionFull text in your LawHub copy of PrepTest 129

Fractal geometry is a mathematical theory devoted to(468 more words not shown)

In the first paragraph, the(11 more words not shown)

Reading the passage

The opening describes self-similarity in fairly abstract terms. Then the Koch curve gives us an example we can work through: replace the middle third, repeat on every new segment, and keep going.

What we’re looking for

My rough prediction is that the construction helps explain what a fractal is. Let's look for a choice that identifies what the example actually shows.

Working the answers

  • A

    Building one fractal from line segments doesn't show that the whole field can be reduced to traditional geometry. No such reduction is argued here.

  • B

    This is a mathematically constructed curve. It isn't introduced as an observed natural form such as a cloud.

  • C

    The description teaches the concept at the beginning. It isn't presented as a reply to the later criticism that the field needs a precise system of theorems and proofs.

  • D
    Correct

    This makes our prediction more specific: the example illustrates self-similarity. Applying the same operation to each smaller segment creates parts resembling the larger pattern. The next paragraph explicitly explains that connection between the construction and self-similarity.

  • E

    The writer has just said an exact definition of fractals hasn't been established. Giving an example with a common property is different from supplying that missing definition.

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